Mendel's Data

Topics Addressed

Estimation of Proportions

Genetics

The person who founded modern
genetics was Gregor Mendel
(for more information on Mendel and his work you can visit
MendelWeb),
who in a series of experiments on
garden peas in about 1865 provided a scientific explanation for heredity
and eventually caused a revolution in human understanding of life.

However, on the basis of a reanalysis of Mendel's
data, a statistician named Fisher some 70 years
later found compelling evidence that someone had fudged Mendel's data so
that the agreement between his genetic theory and the outcome of his
experiments was much too close for comfort. Mendel looked at a number of
characteristics of pea plants, including their seed color and whether the
plants flowered early or late in the season, and one of the things he
noticed was that pea seeds are always either smooth or wrinkled. He bred a
pure smooth strain and a pure wrinkled strain, resulting in first-generation
hybrids, which all turned out to be smooth. He then crossed the first-
generation hybrids with themselves to get second-generation hybrids, some of
which were smooth and some wrinkled. Across his many field trials he put
together data on 7324 second-generation hybrid plants, of which 5474 turned
out to be smooth and 1850 wrinkled. Make up a simple genetic model to
account for these results.

Under this model, what is the chance of
agreement between the observed and expected frequencies of smooth and
wrinkled as close as that reported by Mendel, or closer?

What do you conclude on the basis of this one set of results about whether he
fudged his data?